The former health secretary was speaking during a show on the Edinburgh Festival Fringe.
He had previously admitted there was some “arrogance” around the party’s campaign in 1997, on which he worked, but told host, and former MSP, Neil Findlay that he was not sure if the current party had the same outlook.
Most of the contact, Mr Burnham said, he has with the upper echelons of the party is through “reading briefings about me in the newspapers”.
We have allowed a corrosive, divisive politics to separate people one from another
He added: “We have allowed a corrosive, divisive politics to separate people one from another.”
He continued: “The Labour Party has put itself in a position where it can bring change – and that’s a great thing, congratulations to the people who’ve been there, put us in that position – the Labour Party needs to show how it can bring hope.”
Mr Burnham was twice a contender for the leadership but was beaten both times, first by Ed Miliband and then Jeremy Corbyn.
Asked if he would consider another tilt at the top job, he said the circumstances would have to be right.
Since leaving Westminster, the mayor has turned his sights to reforming politics, telling attendees at the event in Edinburgh’s Freemasons Hall he would like to see the whip system dropped in the Commons, as well as a fundamental “re-wiring” of the UK.
When asked, he said he was enjoying the job of Greater Manchester mayor, where his flagship public transport policy – which will see buses brought into public ownership – is due to come into force later this year.
He added: “I do feel energised – and I do think this thing that we’re building, this conversation we’re building in the regions and the nations, is of more importance.
“This mentality that Westminster is the only show in town and we have to rush back there is actually what’s wrong.”
Mr Burnham said he hoped there would be a Labour government led by Sir Keir Starmer after the next election – which he said would likely be “the most unpleasant, divisive general election that we will have seen in our lifetimes” – that would bring “the hope and that kind of radical change to the way the country is run”.
“If a path opens up in time then, of course, I’m not going to turn away from that,” he added.
“I think there potentially is one last go at Westminster somewhere. But I want to be clear about this – I would only be going back to enact what I’ve talked about today.”